I have seen this be very effective in several pro games. My terran opponents tend to just assume I'm going to FE so they skimp on units for quite a while. While 4-gate does punish this well, I think that the blink all-in is more reliable. Besides, 4-gating is no fun. Can someone give the build order for this? It's not on liquipedia...

I suppose it's because sentries cost a lot of gas (which could decrease stalker production), you have to wait to research Hallucination, and then wait for energy to make a hallucination. Even at that hallucinations are not infinite. With robo, not only do you open the tech path, but its faster and cheaper.